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Question

A small body of super dense material, with mass equal to half of that of earth but whose size is very small compared to that of earth, starts from rest at the height h<<R above the earths surface. It reaches the earths surface in time given by

A
2hg
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B
4h3g
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C
2h3g
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D
hg
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Solution

The correct option is A 4h3g
As the masses are comparable, both the earth and the body will move upto their centre of mass:
M2(x)=M(hx)=x=2h3
Time taken, t=2xg=  2(2h3)g=4h3g

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